Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.180068 | 0.103962 | 0.0519811 | − | 0.998648i | \(-0.483446\pi\) | ||||
0.0519811 | + | 0.998648i | \(0.483446\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.11636 | −1.39368 | −0.696839 | − | 0.717227i | \(-0.745411\pi\) | ||||
−0.696839 | + | 0.717227i | \(0.745411\pi\) | |||||||
\(6\) | −0.180068 | −0.0735124 | ||||||||
\(7\) | 2.83625 | 1.07200 | 0.536001 | − | 0.844217i | \(-0.319934\pi\) | ||||
0.536001 | + | 0.844217i | \(0.319934\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.96758 | −0.989192 | ||||||||
\(10\) | 3.11636 | 0.985479 | ||||||||
\(11\) | 1.84231 | 0.555476 | 0.277738 | − | 0.960657i | \(-0.410415\pi\) | ||||
0.277738 | + | 0.960657i | \(0.410415\pi\) | |||||||
\(12\) | 0.180068 | 0.0519811 | ||||||||
\(13\) | −3.19934 | −0.887338 | −0.443669 | − | 0.896191i | \(-0.646323\pi\) | ||||
−0.443669 | + | 0.896191i | \(0.646323\pi\) | |||||||
\(14\) | −2.83625 | −0.758021 | ||||||||
\(15\) | −0.561156 | −0.144890 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.26163 | 1.27613 | 0.638066 | − | 0.769982i | \(-0.279735\pi\) | ||||
0.638066 | + | 0.769982i | \(0.279735\pi\) | |||||||
\(18\) | 2.96758 | 0.699464 | ||||||||
\(19\) | −2.30746 | −0.529368 | −0.264684 | − | 0.964335i | \(-0.585268\pi\) | ||||
−0.264684 | + | 0.964335i | \(0.585268\pi\) | |||||||
\(20\) | −3.11636 | −0.696839 | ||||||||
\(21\) | 0.510718 | 0.111448 | ||||||||
\(22\) | −1.84231 | −0.392781 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −0.180068 | −0.0367562 | ||||||||
\(25\) | 4.71170 | 0.942340 | ||||||||
\(26\) | 3.19934 | 0.627443 | ||||||||
\(27\) | −1.07457 | −0.206801 | ||||||||
\(28\) | 2.83625 | 0.536001 | ||||||||
\(29\) | −4.19619 | −0.779213 | −0.389606 | − | 0.920981i | \(-0.627389\pi\) | ||||
−0.389606 | + | 0.920981i | \(0.627389\pi\) | |||||||
\(30\) | 0.561156 | 0.102453 | ||||||||
\(31\) | 0.161014 | 0.0289189 | 0.0144595 | − | 0.999895i | \(-0.495397\pi\) | ||||
0.0144595 | + | 0.999895i | \(0.495397\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.331740 | 0.0577486 | ||||||||
\(34\) | −5.26163 | −0.902362 | ||||||||
\(35\) | −8.83879 | −1.49403 | ||||||||
\(36\) | −2.96758 | −0.494596 | ||||||||
\(37\) | 3.37004 | 0.554032 | 0.277016 | − | 0.960865i | \(-0.410655\pi\) | ||||
0.277016 | + | 0.960865i | \(0.410655\pi\) | |||||||
\(38\) | 2.30746 | 0.374320 | ||||||||
\(39\) | −0.576099 | −0.0922496 | ||||||||
\(40\) | 3.11636 | 0.492740 | ||||||||
\(41\) | 7.27050 | 1.13546 | 0.567730 | − | 0.823215i | \(-0.307822\pi\) | ||||
0.567730 | + | 0.823215i | \(0.307822\pi\) | |||||||
\(42\) | −0.510718 | −0.0788055 | ||||||||
\(43\) | −4.10314 | −0.625724 | −0.312862 | − | 0.949799i | \(-0.601288\pi\) | ||||
−0.312862 | + | 0.949799i | \(0.601288\pi\) | |||||||
\(44\) | 1.84231 | 0.277738 | ||||||||
\(45\) | 9.24803 | 1.37862 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 8.67972 | 1.26607 | 0.633033 | − | 0.774125i | \(-0.281810\pi\) | ||||
0.633033 | + | 0.774125i | \(0.281810\pi\) | |||||||
\(48\) | 0.180068 | 0.0259906 | ||||||||
\(49\) | 1.04433 | 0.149190 | ||||||||
\(50\) | −4.71170 | −0.666335 | ||||||||
\(51\) | 0.947450 | 0.132670 | ||||||||
\(52\) | −3.19934 | −0.443669 | ||||||||
\(53\) | −5.41261 | −0.743479 | −0.371740 | − | 0.928337i | \(-0.621239\pi\) | ||||
−0.371740 | + | 0.928337i | \(0.621239\pi\) | |||||||
\(54\) | 1.07457 | 0.146230 | ||||||||
\(55\) | −5.74129 | −0.774155 | ||||||||
\(56\) | −2.83625 | −0.379010 | ||||||||
\(57\) | −0.415500 | −0.0550343 | ||||||||
\(58\) | 4.19619 | 0.550987 | ||||||||
\(59\) | −11.3258 | −1.47449 | −0.737245 | − | 0.675626i | \(-0.763874\pi\) | ||||
−0.737245 | + | 0.675626i | \(0.763874\pi\) | |||||||
\(60\) | −0.561156 | −0.0724450 | ||||||||
\(61\) | 4.07919 | 0.522287 | 0.261143 | − | 0.965300i | \(-0.415900\pi\) | ||||
0.261143 | + | 0.965300i | \(0.415900\pi\) | |||||||
\(62\) | −0.161014 | −0.0204488 | ||||||||
\(63\) | −8.41680 | −1.06042 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.97030 | 1.23666 | ||||||||
\(66\) | −0.331740 | −0.0408344 | ||||||||
\(67\) | −8.82256 | −1.07785 | −0.538924 | − | 0.842355i | \(-0.681169\pi\) | ||||
−0.538924 | + | 0.842355i | \(0.681169\pi\) | |||||||
\(68\) | 5.26163 | 0.638066 | ||||||||
\(69\) | 0.180068 | 0.0216776 | ||||||||
\(70\) | 8.83879 | 1.05644 | ||||||||
\(71\) | 3.83844 | 0.455539 | 0.227769 | − | 0.973715i | \(-0.426857\pi\) | ||||
0.227769 | + | 0.973715i | \(0.426857\pi\) | |||||||
\(72\) | 2.96758 | 0.349732 | ||||||||
\(73\) | −3.38686 | −0.396402 | −0.198201 | − | 0.980161i | \(-0.563510\pi\) | ||||
−0.198201 | + | 0.980161i | \(0.563510\pi\) | |||||||
\(74\) | −3.37004 | −0.391759 | ||||||||
\(75\) | 0.848425 | 0.0979677 | ||||||||
\(76\) | −2.30746 | −0.264684 | ||||||||
\(77\) | 5.22525 | 0.595472 | ||||||||
\(78\) | 0.576099 | 0.0652303 | ||||||||
\(79\) | 15.0426 | 1.69242 | 0.846210 | − | 0.532849i | \(-0.178879\pi\) | ||||
0.846210 | + | 0.532849i | \(0.178879\pi\) | |||||||
\(80\) | −3.11636 | −0.348420 | ||||||||
\(81\) | 8.70923 | 0.967692 | ||||||||
\(82\) | −7.27050 | −0.802892 | ||||||||
\(83\) | 14.6578 | 1.60891 | 0.804453 | − | 0.594016i | \(-0.202458\pi\) | ||||
0.804453 | + | 0.594016i | \(0.202458\pi\) | |||||||
\(84\) | 0.510718 | 0.0557239 | ||||||||
\(85\) | −16.3971 | −1.77852 | ||||||||
\(86\) | 4.10314 | 0.442453 | ||||||||
\(87\) | −0.755599 | −0.0810087 | ||||||||
\(88\) | −1.84231 | −0.196391 | ||||||||
\(89\) | 4.17165 | 0.442194 | 0.221097 | − | 0.975252i | \(-0.429036\pi\) | ||||
0.221097 | + | 0.975252i | \(0.429036\pi\) | |||||||
\(90\) | −9.24803 | −0.974828 | ||||||||
\(91\) | −9.07414 | −0.951229 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 0.0289934 | 0.00300648 | ||||||||
\(94\) | −8.67972 | −0.895244 | ||||||||
\(95\) | 7.19088 | 0.737769 | ||||||||
\(96\) | −0.180068 | −0.0183781 | ||||||||
\(97\) | −0.272963 | −0.0277152 | −0.0138576 | − | 0.999904i | \(-0.504411\pi\) | ||||
−0.0138576 | + | 0.999904i | \(0.504411\pi\) | |||||||
\(98\) | −1.04433 | −0.105494 | ||||||||
\(99\) | −5.46718 | −0.549473 | ||||||||
\(100\) | 4.71170 | 0.471170 | ||||||||
\(101\) | −1.72561 | −0.171704 | −0.0858521 | − | 0.996308i | \(-0.527361\pi\) | ||||
−0.0858521 | + | 0.996308i | \(0.527361\pi\) | |||||||
\(102\) | −0.947450 | −0.0938115 | ||||||||
\(103\) | −15.7235 | −1.54929 | −0.774643 | − | 0.632399i | \(-0.782070\pi\) | ||||
−0.774643 | + | 0.632399i | \(0.782070\pi\) | |||||||
\(104\) | 3.19934 | 0.313721 | ||||||||
\(105\) | −1.59158 | −0.155322 | ||||||||
\(106\) | 5.41261 | 0.525719 | ||||||||
\(107\) | 8.87665 | 0.858138 | 0.429069 | − | 0.903272i | \(-0.358842\pi\) | ||||
0.429069 | + | 0.903272i | \(0.358842\pi\) | |||||||
\(108\) | −1.07457 | −0.103400 | ||||||||
\(109\) | −12.2645 | −1.17472 | −0.587361 | − | 0.809325i | \(-0.699833\pi\) | ||||
−0.587361 | + | 0.809325i | \(0.699833\pi\) | |||||||
\(110\) | 5.74129 | 0.547410 | ||||||||
\(111\) | 0.606836 | 0.0575984 | ||||||||
\(112\) | 2.83625 | 0.268001 | ||||||||
\(113\) | −15.2526 | −1.43485 | −0.717424 | − | 0.696637i | \(-0.754679\pi\) | ||||
−0.717424 | + | 0.696637i | \(0.754679\pi\) | |||||||
\(114\) | 0.415500 | 0.0389151 | ||||||||
\(115\) | −3.11636 | −0.290602 | ||||||||
\(116\) | −4.19619 | −0.389606 | ||||||||
\(117\) | 9.49429 | 0.877747 | ||||||||
\(118\) | 11.3258 | 1.04262 | ||||||||
\(119\) | 14.9233 | 1.36802 | ||||||||
\(120\) | 0.561156 | 0.0512263 | ||||||||
\(121\) | −7.60591 | −0.691446 | ||||||||
\(122\) | −4.07919 | −0.369312 | ||||||||
\(123\) | 1.30918 | 0.118045 | ||||||||
\(124\) | 0.161014 | 0.0144595 | ||||||||
\(125\) | 0.898453 | 0.0803601 | ||||||||
\(126\) | 8.41680 | 0.749828 | ||||||||
\(127\) | −3.70620 | −0.328872 | −0.164436 | − | 0.986388i | \(-0.552580\pi\) | ||||
−0.164436 | + | 0.986388i | \(0.552580\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.738844 | −0.0650516 | ||||||||
\(130\) | −9.97030 | −0.874453 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | 0.331740 | 0.0288743 | ||||||||
\(133\) | −6.54454 | −0.567484 | ||||||||
\(134\) | 8.82256 | 0.762153 | ||||||||
\(135\) | 3.34874 | 0.288214 | ||||||||
\(136\) | −5.26163 | −0.451181 | ||||||||
\(137\) | 6.34452 | 0.542049 | 0.271025 | − | 0.962572i | \(-0.412638\pi\) | ||||
0.271025 | + | 0.962572i | \(0.412638\pi\) | |||||||
\(138\) | −0.180068 | −0.0153284 | ||||||||
\(139\) | −0.627932 | −0.0532605 | −0.0266302 | − | 0.999645i | \(-0.508478\pi\) | ||||
−0.0266302 | + | 0.999645i | \(0.508478\pi\) | |||||||
\(140\) | −8.83879 | −0.747014 | ||||||||
\(141\) | 1.56294 | 0.131623 | ||||||||
\(142\) | −3.83844 | −0.322115 | ||||||||
\(143\) | −5.89417 | −0.492895 | ||||||||
\(144\) | −2.96758 | −0.247298 | ||||||||
\(145\) | 13.0768 | 1.08597 | ||||||||
\(146\) | 3.38686 | 0.280299 | ||||||||
\(147\) | 0.188051 | 0.0155102 | ||||||||
\(148\) | 3.37004 | 0.277016 | ||||||||
\(149\) | −7.01246 | −0.574483 | −0.287242 | − | 0.957858i | \(-0.592738\pi\) | ||||
−0.287242 | + | 0.957858i | \(0.592738\pi\) | |||||||
\(150\) | −0.848425 | −0.0692736 | ||||||||
\(151\) | 10.1219 | 0.823708 | 0.411854 | − | 0.911250i | \(-0.364881\pi\) | ||||
0.411854 | + | 0.911250i | \(0.364881\pi\) | |||||||
\(152\) | 2.30746 | 0.187160 | ||||||||
\(153\) | −15.6143 | −1.26234 | ||||||||
\(154\) | −5.22525 | −0.421062 | ||||||||
\(155\) | −0.501777 | −0.0403037 | ||||||||
\(156\) | −0.576099 | −0.0461248 | ||||||||
\(157\) | −18.1972 | −1.45230 | −0.726148 | − | 0.687538i | \(-0.758691\pi\) | ||||
−0.726148 | + | 0.687538i | \(0.758691\pi\) | |||||||
\(158\) | −15.0426 | −1.19672 | ||||||||
\(159\) | −0.974637 | −0.0772938 | ||||||||
\(160\) | 3.11636 | 0.246370 | ||||||||
\(161\) | 2.83625 | 0.223528 | ||||||||
\(162\) | −8.70923 | −0.684262 | ||||||||
\(163\) | 1.13547 | 0.0889369 | 0.0444684 | − | 0.999011i | \(-0.485841\pi\) | ||||
0.0444684 | + | 0.999011i | \(0.485841\pi\) | |||||||
\(164\) | 7.27050 | 0.567730 | ||||||||
\(165\) | −1.03382 | −0.0804829 | ||||||||
\(166\) | −14.6578 | −1.13767 | ||||||||
\(167\) | 9.90036 | 0.766113 | 0.383056 | − | 0.923725i | \(-0.374871\pi\) | ||||
0.383056 | + | 0.923725i | \(0.374871\pi\) | |||||||
\(168\) | −0.510718 | −0.0394028 | ||||||||
\(169\) | −2.76421 | −0.212632 | ||||||||
\(170\) | 16.3971 | 1.25760 | ||||||||
\(171\) | 6.84756 | 0.523646 | ||||||||
\(172\) | −4.10314 | −0.312862 | ||||||||
\(173\) | −20.3169 | −1.54466 | −0.772331 | − | 0.635220i | \(-0.780909\pi\) | ||||
−0.772331 | + | 0.635220i | \(0.780909\pi\) | |||||||
\(174\) | 0.755599 | 0.0572818 | ||||||||
\(175\) | 13.3636 | 1.01019 | ||||||||
\(176\) | 1.84231 | 0.138869 | ||||||||
\(177\) | −2.03941 | −0.153291 | ||||||||
\(178\) | −4.17165 | −0.312678 | ||||||||
\(179\) | 11.1814 | 0.835734 | 0.417867 | − | 0.908508i | \(-0.362778\pi\) | ||||
0.417867 | + | 0.908508i | \(0.362778\pi\) | |||||||
\(180\) | 9.24803 | 0.689308 | ||||||||
\(181\) | −2.66605 | −0.198166 | −0.0990828 | − | 0.995079i | \(-0.531591\pi\) | ||||
−0.0990828 | + | 0.995079i | \(0.531591\pi\) | |||||||
\(182\) | 9.07414 | 0.672620 | ||||||||
\(183\) | 0.734531 | 0.0542981 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −10.5023 | −0.772142 | ||||||||
\(186\) | −0.0289934 | −0.00212590 | ||||||||
\(187\) | 9.69353 | 0.708861 | ||||||||
\(188\) | 8.67972 | 0.633033 | ||||||||
\(189\) | −3.04775 | −0.221691 | ||||||||
\(190\) | −7.19088 | −0.521681 | ||||||||
\(191\) | 1.79571 | 0.129933 | 0.0649665 | − | 0.997887i | \(-0.479306\pi\) | ||||
0.0649665 | + | 0.997887i | \(0.479306\pi\) | |||||||
\(192\) | 0.180068 | 0.0129953 | ||||||||
\(193\) | −7.22308 | −0.519929 | −0.259964 | − | 0.965618i | \(-0.583711\pi\) | ||||
−0.259964 | + | 0.965618i | \(0.583711\pi\) | |||||||
\(194\) | 0.272963 | 0.0195976 | ||||||||
\(195\) | 1.79533 | 0.128566 | ||||||||
\(196\) | 1.04433 | 0.0745952 | ||||||||
\(197\) | 15.2774 | 1.08847 | 0.544233 | − | 0.838934i | \(-0.316821\pi\) | ||||
0.544233 | + | 0.838934i | \(0.316821\pi\) | |||||||
\(198\) | 5.46718 | 0.388536 | ||||||||
\(199\) | −4.82621 | −0.342121 | −0.171060 | − | 0.985261i | \(-0.554719\pi\) | ||||
−0.171060 | + | 0.985261i | \(0.554719\pi\) | |||||||
\(200\) | −4.71170 | −0.333167 | ||||||||
\(201\) | −1.58866 | −0.112055 | ||||||||
\(202\) | 1.72561 | 0.121413 | ||||||||
\(203\) | −11.9015 | −0.835319 | ||||||||
\(204\) | 0.947450 | 0.0663348 | ||||||||
\(205\) | −22.6575 | −1.58247 | ||||||||
\(206\) | 15.7235 | 1.09551 | ||||||||
\(207\) | −2.96758 | −0.206261 | ||||||||
\(208\) | −3.19934 | −0.221834 | ||||||||
\(209\) | −4.25105 | −0.294051 | ||||||||
\(210\) | 1.59158 | 0.109830 | ||||||||
\(211\) | 15.1183 | 1.04078 | 0.520392 | − | 0.853928i | \(-0.325786\pi\) | ||||
0.520392 | + | 0.853928i | \(0.325786\pi\) | |||||||
\(212\) | −5.41261 | −0.371740 | ||||||||
\(213\) | 0.691180 | 0.0473588 | ||||||||
\(214\) | −8.87665 | −0.606795 | ||||||||
\(215\) | 12.7869 | 0.872058 | ||||||||
\(216\) | 1.07457 | 0.0731151 | ||||||||
\(217\) | 0.456676 | 0.0310012 | ||||||||
\(218\) | 12.2645 | 0.830654 | ||||||||
\(219\) | −0.609865 | −0.0412108 | ||||||||
\(220\) | −5.74129 | −0.387078 | ||||||||
\(221\) | −16.8337 | −1.13236 | ||||||||
\(222\) | −0.606836 | −0.0407282 | ||||||||
\(223\) | 6.41023 | 0.429261 | 0.214631 | − | 0.976695i | \(-0.431145\pi\) | ||||
0.214631 | + | 0.976695i | \(0.431145\pi\) | |||||||
\(224\) | −2.83625 | −0.189505 | ||||||||
\(225\) | −13.9823 | −0.932155 | ||||||||
\(226\) | 15.2526 | 1.01459 | ||||||||
\(227\) | −24.4650 | −1.62380 | −0.811898 | − | 0.583799i | \(-0.801566\pi\) | ||||
−0.811898 | + | 0.583799i | \(0.801566\pi\) | |||||||
\(228\) | −0.415500 | −0.0275171 | ||||||||
\(229\) | −28.7523 | −1.90001 | −0.950003 | − | 0.312242i | \(-0.898920\pi\) | ||||
−0.950003 | + | 0.312242i | \(0.898920\pi\) | |||||||
\(230\) | 3.11636 | 0.205487 | ||||||||
\(231\) | 0.940899 | 0.0619066 | ||||||||
\(232\) | 4.19619 | 0.275493 | ||||||||
\(233\) | −15.9419 | −1.04439 | −0.522195 | − | 0.852826i | \(-0.674887\pi\) | ||||
−0.522195 | + | 0.852826i | \(0.674887\pi\) | |||||||
\(234\) | −9.49429 | −0.620661 | ||||||||
\(235\) | −27.0491 | −1.76449 | ||||||||
\(236\) | −11.3258 | −0.737245 | ||||||||
\(237\) | 2.70868 | 0.175948 | ||||||||
\(238\) | −14.9233 | −0.967335 | ||||||||
\(239\) | −11.9789 | −0.774852 | −0.387426 | − | 0.921901i | \(-0.626636\pi\) | ||||
−0.387426 | + | 0.921901i | \(0.626636\pi\) | |||||||
\(240\) | −0.561156 | −0.0362225 | ||||||||
\(241\) | −7.44765 | −0.479745 | −0.239873 | − | 0.970804i | \(-0.577106\pi\) | ||||
−0.239873 | + | 0.970804i | \(0.577106\pi\) | |||||||
\(242\) | 7.60591 | 0.488926 | ||||||||
\(243\) | 4.79196 | 0.307404 | ||||||||
\(244\) | 4.07919 | 0.261143 | ||||||||
\(245\) | −3.25452 | −0.207923 | ||||||||
\(246\) | −1.30918 | −0.0834705 | ||||||||
\(247\) | 7.38236 | 0.469728 | ||||||||
\(248\) | −0.161014 | −0.0102244 | ||||||||
\(249\) | 2.63941 | 0.167266 | ||||||||
\(250\) | −0.898453 | −0.0568232 | ||||||||
\(251\) | −8.65134 | −0.546068 | −0.273034 | − | 0.962004i | \(-0.588027\pi\) | ||||
−0.273034 | + | 0.962004i | \(0.588027\pi\) | |||||||
\(252\) | −8.41680 | −0.530208 | ||||||||
\(253\) | 1.84231 | 0.115825 | ||||||||
\(254\) | 3.70620 | 0.232548 | ||||||||
\(255\) | −2.95260 | −0.184899 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.12698 | 0.195056 | 0.0975279 | − | 0.995233i | \(-0.468906\pi\) | ||||
0.0975279 | + | 0.995233i | \(0.468906\pi\) | |||||||
\(258\) | 0.738844 | 0.0459984 | ||||||||
\(259\) | 9.55829 | 0.593924 | ||||||||
\(260\) | 9.97030 | 0.618332 | ||||||||
\(261\) | 12.4525 | 0.770791 | ||||||||
\(262\) | −1.00000 | −0.0617802 | ||||||||
\(263\) | 4.74709 | 0.292718 | 0.146359 | − | 0.989232i | \(-0.453244\pi\) | ||||
0.146359 | + | 0.989232i | \(0.453244\pi\) | |||||||
\(264\) | −0.331740 | −0.0204172 | ||||||||
\(265\) | 16.8676 | 1.03617 | ||||||||
\(266\) | 6.54454 | 0.401272 | ||||||||
\(267\) | 0.751179 | 0.0459714 | ||||||||
\(268\) | −8.82256 | −0.538924 | ||||||||
\(269\) | 14.5561 | 0.887504 | 0.443752 | − | 0.896150i | \(-0.353647\pi\) | ||||
0.443752 | + | 0.896150i | \(0.353647\pi\) | |||||||
\(270\) | −3.34874 | −0.203798 | ||||||||
\(271\) | 9.44993 | 0.574042 | 0.287021 | − | 0.957924i | \(-0.407335\pi\) | ||||
0.287021 | + | 0.957924i | \(0.407335\pi\) | |||||||
\(272\) | 5.26163 | 0.319033 | ||||||||
\(273\) | −1.63396 | −0.0988919 | ||||||||
\(274\) | −6.34452 | −0.383287 | ||||||||
\(275\) | 8.68039 | 0.523447 | ||||||||
\(276\) | 0.180068 | 0.0108388 | ||||||||
\(277\) | −11.7380 | −0.705265 | −0.352633 | − | 0.935762i | \(-0.614713\pi\) | ||||
−0.352633 | + | 0.935762i | \(0.614713\pi\) | |||||||
\(278\) | 0.627932 | 0.0376608 | ||||||||
\(279\) | −0.477821 | −0.0286064 | ||||||||
\(280\) | 8.83879 | 0.528218 | ||||||||
\(281\) | 5.06304 | 0.302036 | 0.151018 | − | 0.988531i | \(-0.451745\pi\) | ||||
0.151018 | + | 0.988531i | \(0.451745\pi\) | |||||||
\(282\) | −1.56294 | −0.0930716 | ||||||||
\(283\) | 3.36418 | 0.199980 | 0.0999898 | − | 0.994988i | \(-0.468119\pi\) | ||||
0.0999898 | + | 0.994988i | \(0.468119\pi\) | |||||||
\(284\) | 3.83844 | 0.227769 | ||||||||
\(285\) | 1.29485 | 0.0767001 | ||||||||
\(286\) | 5.89417 | 0.348529 | ||||||||
\(287\) | 20.6210 | 1.21722 | ||||||||
\(288\) | 2.96758 | 0.174866 | ||||||||
\(289\) | 10.6847 | 0.628513 | ||||||||
\(290\) | −13.0768 | −0.767898 | ||||||||
\(291\) | −0.0491518 | −0.00288133 | ||||||||
\(292\) | −3.38686 | −0.198201 | ||||||||
\(293\) | −24.6029 | −1.43732 | −0.718659 | − | 0.695363i | \(-0.755244\pi\) | ||||
−0.718659 | + | 0.695363i | \(0.755244\pi\) | |||||||
\(294\) | −0.188051 | −0.0109673 | ||||||||
\(295\) | 35.2952 | 2.05496 | ||||||||
\(296\) | −3.37004 | −0.195880 | ||||||||
\(297\) | −1.97968 | −0.114873 | ||||||||
\(298\) | 7.01246 | 0.406221 | ||||||||
\(299\) | −3.19934 | −0.185023 | ||||||||
\(300\) | 0.848425 | 0.0489839 | ||||||||
\(301\) | −11.6376 | −0.670778 | ||||||||
\(302\) | −10.1219 | −0.582449 | ||||||||
\(303\) | −0.310726 | −0.0178508 | ||||||||
\(304\) | −2.30746 | −0.132342 | ||||||||
\(305\) | −12.7122 | −0.727900 | ||||||||
\(306\) | 15.6143 | 0.892609 | ||||||||
\(307\) | −22.2355 | −1.26905 | −0.634524 | − | 0.772903i | \(-0.718804\pi\) | ||||
−0.634524 | + | 0.772903i | \(0.718804\pi\) | |||||||
\(308\) | 5.22525 | 0.297736 | ||||||||
\(309\) | −2.83130 | −0.161067 | ||||||||
\(310\) | 0.501777 | 0.0284990 | ||||||||
\(311\) | −21.8598 | −1.23956 | −0.619778 | − | 0.784777i | \(-0.712777\pi\) | ||||
−0.619778 | + | 0.784777i | \(0.712777\pi\) | |||||||
\(312\) | 0.576099 | 0.0326152 | ||||||||
\(313\) | 1.35107 | 0.0763670 | 0.0381835 | − | 0.999271i | \(-0.487843\pi\) | ||||
0.0381835 | + | 0.999271i | \(0.487843\pi\) | |||||||
\(314\) | 18.1972 | 1.02693 | ||||||||
\(315\) | 26.2298 | 1.47788 | ||||||||
\(316\) | 15.0426 | 0.846210 | ||||||||
\(317\) | 13.8256 | 0.776525 | 0.388262 | − | 0.921549i | \(-0.373075\pi\) | ||||
0.388262 | + | 0.921549i | \(0.373075\pi\) | |||||||
\(318\) | 0.974637 | 0.0546549 | ||||||||
\(319\) | −7.73067 | −0.432834 | ||||||||
\(320\) | −3.11636 | −0.174210 | ||||||||
\(321\) | 1.59840 | 0.0892139 | ||||||||
\(322\) | −2.83625 | −0.158058 | ||||||||
\(323\) | −12.1410 | −0.675543 | ||||||||
\(324\) | 8.70923 | 0.483846 | ||||||||
\(325\) | −15.0743 | −0.836174 | ||||||||
\(326\) | −1.13547 | −0.0628879 | ||||||||
\(327\) | −2.20843 | −0.122127 | ||||||||
\(328\) | −7.27050 | −0.401446 | ||||||||
\(329\) | 24.6179 | 1.35723 | ||||||||
\(330\) | 1.03382 | 0.0569100 | ||||||||
\(331\) | 0.802881 | 0.0441303 | 0.0220652 | − | 0.999757i | \(-0.492976\pi\) | ||||
0.0220652 | + | 0.999757i | \(0.492976\pi\) | |||||||
\(332\) | 14.6578 | 0.804453 | ||||||||
\(333\) | −10.0009 | −0.548044 | ||||||||
\(334\) | −9.90036 | −0.541724 | ||||||||
\(335\) | 27.4943 | 1.50217 | ||||||||
\(336\) | 0.510718 | 0.0278620 | ||||||||
\(337\) | −20.0302 | −1.09111 | −0.545557 | − | 0.838074i | \(-0.683682\pi\) | ||||
−0.545557 | + | 0.838074i | \(0.683682\pi\) | |||||||
\(338\) | 2.76421 | 0.150353 | ||||||||
\(339\) | −2.74651 | −0.149170 | ||||||||
\(340\) | −16.3971 | −0.889259 | ||||||||
\(341\) | 0.296637 | 0.0160638 | ||||||||
\(342\) | −6.84756 | −0.370274 | ||||||||
\(343\) | −16.8918 | −0.912070 | ||||||||
\(344\) | 4.10314 | 0.221227 | ||||||||
\(345\) | −0.561156 | −0.0302116 | ||||||||
\(346\) | 20.3169 | 1.09224 | ||||||||
\(347\) | 0.578901 | 0.0310770 | 0.0155385 | − | 0.999879i | \(-0.495054\pi\) | ||||
0.0155385 | + | 0.999879i | \(0.495054\pi\) | |||||||
\(348\) | −0.755599 | −0.0405044 | ||||||||
\(349\) | −25.7649 | −1.37916 | −0.689581 | − | 0.724209i | \(-0.742205\pi\) | ||||
−0.689581 | + | 0.724209i | \(0.742205\pi\) | |||||||
\(350\) | −13.3636 | −0.714313 | ||||||||
\(351\) | 3.43791 | 0.183502 | ||||||||
\(352\) | −1.84231 | −0.0981953 | ||||||||
\(353\) | −17.6860 | −0.941332 | −0.470666 | − | 0.882312i | \(-0.655986\pi\) | ||||
−0.470666 | + | 0.882312i | \(0.655986\pi\) | |||||||
\(354\) | 2.03941 | 0.108393 | ||||||||
\(355\) | −11.9620 | −0.634875 | ||||||||
\(356\) | 4.17165 | 0.221097 | ||||||||
\(357\) | 2.68721 | 0.142222 | ||||||||
\(358\) | −11.1814 | −0.590953 | ||||||||
\(359\) | 11.8894 | 0.627497 | 0.313749 | − | 0.949506i | \(-0.398415\pi\) | ||||
0.313749 | + | 0.949506i | \(0.398415\pi\) | |||||||
\(360\) | −9.24803 | −0.487414 | ||||||||
\(361\) | −13.6756 | −0.719770 | ||||||||
\(362\) | 2.66605 | 0.140124 | ||||||||
\(363\) | −1.36958 | −0.0718843 | ||||||||
\(364\) | −9.07414 | −0.475614 | ||||||||
\(365\) | 10.5547 | 0.552457 | ||||||||
\(366\) | −0.734531 | −0.0383945 | ||||||||
\(367\) | 7.26661 | 0.379314 | 0.189657 | − | 0.981850i | \(-0.439262\pi\) | ||||
0.189657 | + | 0.981850i | \(0.439262\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −21.5757 | −1.12319 | ||||||||
\(370\) | 10.5023 | 0.545987 | ||||||||
\(371\) | −15.3515 | −0.797012 | ||||||||
\(372\) | 0.0289934 | 0.00150324 | ||||||||
\(373\) | −13.5275 | −0.700430 | −0.350215 | − | 0.936669i | \(-0.613891\pi\) | ||||
−0.350215 | + | 0.936669i | \(0.613891\pi\) | |||||||
\(374\) | −9.69353 | −0.501241 | ||||||||
\(375\) | 0.161783 | 0.00835442 | ||||||||
\(376\) | −8.67972 | −0.447622 | ||||||||
\(377\) | 13.4250 | 0.691425 | ||||||||
\(378\) | 3.04775 | 0.156759 | ||||||||
\(379\) | 12.8909 | 0.662162 | 0.331081 | − | 0.943602i | \(-0.392587\pi\) | ||||
0.331081 | + | 0.943602i | \(0.392587\pi\) | |||||||
\(380\) | 7.19088 | 0.368884 | ||||||||
\(381\) | −0.667368 | −0.0341903 | ||||||||
\(382\) | −1.79571 | −0.0918766 | ||||||||
\(383\) | −8.96319 | −0.457998 | −0.228999 | − | 0.973427i | \(-0.573545\pi\) | ||||
−0.228999 | + | 0.973427i | \(0.573545\pi\) | |||||||
\(384\) | −0.180068 | −0.00918905 | ||||||||
\(385\) | −16.2838 | −0.829897 | ||||||||
\(386\) | 7.22308 | 0.367645 | ||||||||
\(387\) | 12.1764 | 0.618961 | ||||||||
\(388\) | −0.272963 | −0.0138576 | ||||||||
\(389\) | −28.0289 | −1.42112 | −0.710560 | − | 0.703636i | \(-0.751558\pi\) | ||||
−0.710560 | + | 0.703636i | \(0.751558\pi\) | |||||||
\(390\) | −1.79533 | −0.0909101 | ||||||||
\(391\) | 5.26163 | 0.266092 | ||||||||
\(392\) | −1.04433 | −0.0527468 | ||||||||
\(393\) | 0.180068 | 0.00908322 | ||||||||
\(394\) | −15.2774 | −0.769662 | ||||||||
\(395\) | −46.8780 | −2.35869 | ||||||||
\(396\) | −5.46718 | −0.274736 | ||||||||
\(397\) | 20.6532 | 1.03656 | 0.518278 | − | 0.855212i | \(-0.326573\pi\) | ||||
0.518278 | + | 0.855212i | \(0.326573\pi\) | |||||||
\(398\) | 4.82621 | 0.241916 | ||||||||
\(399\) | −1.17846 | −0.0589969 | ||||||||
\(400\) | 4.71170 | 0.235585 | ||||||||
\(401\) | −21.1495 | −1.05615 | −0.528077 | − | 0.849197i | \(-0.677087\pi\) | ||||
−0.528077 | + | 0.849197i | \(0.677087\pi\) | |||||||
\(402\) | 1.58866 | 0.0792351 | ||||||||
\(403\) | −0.515139 | −0.0256609 | ||||||||
\(404\) | −1.72561 | −0.0858521 | ||||||||
\(405\) | −27.1411 | −1.34865 | ||||||||
\(406\) | 11.9015 | 0.590659 | ||||||||
\(407\) | 6.20865 | 0.307751 | ||||||||
\(408\) | −0.947450 | −0.0469058 | ||||||||
\(409\) | 7.40738 | 0.366271 | 0.183136 | − | 0.983088i | \(-0.441375\pi\) | ||||
0.183136 | + | 0.983088i | \(0.441375\pi\) | |||||||
\(410\) | 22.6575 | 1.11897 | ||||||||
\(411\) | 1.14244 | 0.0563526 | ||||||||
\(412\) | −15.7235 | −0.774643 | ||||||||
\(413\) | −32.1228 | −1.58066 | ||||||||
\(414\) | 2.96758 | 0.145848 | ||||||||
\(415\) | −45.6791 | −2.24230 | ||||||||
\(416\) | 3.19934 | 0.156861 | ||||||||
\(417\) | −0.113070 | −0.00553708 | ||||||||
\(418\) | 4.25105 | 0.207926 | ||||||||
\(419\) | −31.3233 | −1.53024 | −0.765122 | − | 0.643885i | \(-0.777321\pi\) | ||||
−0.765122 | + | 0.643885i | \(0.777321\pi\) | |||||||
\(420\) | −1.59158 | −0.0776612 | ||||||||
\(421\) | −25.1680 | −1.22661 | −0.613305 | − | 0.789846i | \(-0.710161\pi\) | ||||
−0.613305 | + | 0.789846i | \(0.710161\pi\) | |||||||
\(422\) | −15.1183 | −0.735945 | ||||||||
\(423\) | −25.7577 | −1.25238 | ||||||||
\(424\) | 5.41261 | 0.262860 | ||||||||
\(425\) | 24.7912 | 1.20255 | ||||||||
\(426\) | −0.691180 | −0.0334878 | ||||||||
\(427\) | 11.5696 | 0.559893 | ||||||||
\(428\) | 8.87665 | 0.429069 | ||||||||
\(429\) | −1.06135 | −0.0512425 | ||||||||
\(430\) | −12.7869 | −0.616638 | ||||||||
\(431\) | 20.4496 | 0.985021 | 0.492511 | − | 0.870306i | \(-0.336079\pi\) | ||||
0.492511 | + | 0.870306i | \(0.336079\pi\) | |||||||
\(432\) | −1.07457 | −0.0517002 | ||||||||
\(433\) | 13.6040 | 0.653765 | 0.326882 | − | 0.945065i | \(-0.394002\pi\) | ||||
0.326882 | + | 0.945065i | \(0.394002\pi\) | |||||||
\(434\) | −0.456676 | −0.0219212 | ||||||||
\(435\) | 2.35472 | 0.112900 | ||||||||
\(436\) | −12.2645 | −0.587361 | ||||||||
\(437\) | −2.30746 | −0.110381 | ||||||||
\(438\) | 0.609865 | 0.0291405 | ||||||||
\(439\) | −9.19695 | −0.438947 | −0.219473 | − | 0.975619i | \(-0.570434\pi\) | ||||
−0.219473 | + | 0.975619i | \(0.570434\pi\) | |||||||
\(440\) | 5.74129 | 0.273705 | ||||||||
\(441\) | −3.09914 | −0.147578 | ||||||||
\(442\) | 16.8337 | 0.800700 | ||||||||
\(443\) | −9.54765 | −0.453622 | −0.226811 | − | 0.973939i | \(-0.572830\pi\) | ||||
−0.226811 | + | 0.973939i | \(0.572830\pi\) | |||||||
\(444\) | 0.606836 | 0.0287992 | ||||||||
\(445\) | −13.0004 | −0.616276 | ||||||||
\(446\) | −6.41023 | −0.303533 | ||||||||
\(447\) | −1.26272 | −0.0597245 | ||||||||
\(448\) | 2.83625 | 0.134000 | ||||||||
\(449\) | 2.94871 | 0.139158 | 0.0695792 | − | 0.997576i | \(-0.477834\pi\) | ||||
0.0695792 | + | 0.997576i | \(0.477834\pi\) | |||||||
\(450\) | 13.9823 | 0.659133 | ||||||||
\(451\) | 13.3945 | 0.630722 | ||||||||
\(452\) | −15.2526 | −0.717424 | ||||||||
\(453\) | 1.82263 | 0.0856345 | ||||||||
\(454\) | 24.4650 | 1.14820 | ||||||||
\(455\) | 28.2783 | 1.32571 | ||||||||
\(456\) | 0.415500 | 0.0194575 | ||||||||
\(457\) | −27.5060 | −1.28668 | −0.643338 | − | 0.765582i | \(-0.722451\pi\) | ||||
−0.643338 | + | 0.765582i | \(0.722451\pi\) | |||||||
\(458\) | 28.7523 | 1.34351 | ||||||||
\(459\) | −5.65398 | −0.263905 | ||||||||
\(460\) | −3.11636 | −0.145301 | ||||||||
\(461\) | 37.7226 | 1.75692 | 0.878459 | − | 0.477818i | \(-0.158572\pi\) | ||||
0.878459 | + | 0.477818i | \(0.158572\pi\) | |||||||
\(462\) | −0.940899 | −0.0437746 | ||||||||
\(463\) | −4.23431 | −0.196785 | −0.0983925 | − | 0.995148i | \(-0.531370\pi\) | ||||
−0.0983925 | + | 0.995148i | \(0.531370\pi\) | |||||||
\(464\) | −4.19619 | −0.194803 | ||||||||
\(465\) | −0.0903540 | −0.00419006 | ||||||||
\(466\) | 15.9419 | 0.738495 | ||||||||
\(467\) | −18.2718 | −0.845519 | −0.422759 | − | 0.906242i | \(-0.638938\pi\) | ||||
−0.422759 | + | 0.906242i | \(0.638938\pi\) | |||||||
\(468\) | 9.49429 | 0.438874 | ||||||||
\(469\) | −25.0230 | −1.15546 | ||||||||
\(470\) | 27.0491 | 1.24768 | ||||||||
\(471\) | −3.27674 | −0.150984 | ||||||||
\(472\) | 11.3258 | 0.521311 | ||||||||
\(473\) | −7.55925 | −0.347575 | ||||||||
\(474\) | −2.70868 | −0.124414 | ||||||||
\(475\) | −10.8721 | −0.498844 | ||||||||
\(476\) | 14.9233 | 0.684009 | ||||||||
\(477\) | 16.0623 | 0.735444 | ||||||||
\(478\) | 11.9789 | 0.547903 | ||||||||
\(479\) | −7.83957 | −0.358199 | −0.179100 | − | 0.983831i | \(-0.557318\pi\) | ||||
−0.179100 | + | 0.983831i | \(0.557318\pi\) | |||||||
\(480\) | 0.561156 | 0.0256132 | ||||||||
\(481\) | −10.7819 | −0.491613 | ||||||||
\(482\) | 7.44765 | 0.339231 | ||||||||
\(483\) | 0.510718 | 0.0232385 | ||||||||
\(484\) | −7.60591 | −0.345723 | ||||||||
\(485\) | 0.850650 | 0.0386260 | ||||||||
\(486\) | −4.79196 | −0.217368 | ||||||||
\(487\) | −2.46633 | −0.111760 | −0.0558801 | − | 0.998437i | \(-0.517796\pi\) | ||||
−0.0558801 | + | 0.998437i | \(0.517796\pi\) | |||||||
\(488\) | −4.07919 | −0.184656 | ||||||||
\(489\) | 0.204462 | 0.00924608 | ||||||||
\(490\) | 3.25452 | 0.147024 | ||||||||
\(491\) | 10.0832 | 0.455050 | 0.227525 | − | 0.973772i | \(-0.426937\pi\) | ||||
0.227525 | + | 0.973772i | \(0.426937\pi\) | |||||||
\(492\) | 1.30918 | 0.0590225 | ||||||||
\(493\) | −22.0788 | −0.994379 | ||||||||
\(494\) | −7.38236 | −0.332148 | ||||||||
\(495\) | 17.0377 | 0.765788 | ||||||||
\(496\) | 0.161014 | 0.00722974 | ||||||||
\(497\) | 10.8868 | 0.488339 | ||||||||
\(498\) | −2.63941 | −0.118275 | ||||||||
\(499\) | −26.8782 | −1.20323 | −0.601616 | − | 0.798785i | \(-0.705476\pi\) | ||||
−0.601616 | + | 0.798785i | \(0.705476\pi\) | |||||||
\(500\) | 0.898453 | 0.0401801 | ||||||||
\(501\) | 1.78274 | 0.0796468 | ||||||||
\(502\) | 8.65134 | 0.386128 | ||||||||
\(503\) | 14.1835 | 0.632412 | 0.316206 | − | 0.948691i | \(-0.397591\pi\) | ||||
0.316206 | + | 0.948691i | \(0.397591\pi\) | |||||||
\(504\) | 8.41680 | 0.374914 | ||||||||
\(505\) | 5.37761 | 0.239301 | ||||||||
\(506\) | −1.84231 | −0.0819005 | ||||||||
\(507\) | −0.497746 | −0.0221057 | ||||||||
\(508\) | −3.70620 | −0.164436 | ||||||||
\(509\) | 26.0094 | 1.15285 | 0.576423 | − | 0.817151i | \(-0.304448\pi\) | ||||
0.576423 | + | 0.817151i | \(0.304448\pi\) | |||||||
\(510\) | 2.95260 | 0.130743 | ||||||||
\(511\) | −9.60600 | −0.424944 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.47953 | 0.109474 | ||||||||
\(514\) | −3.12698 | −0.137925 | ||||||||
\(515\) | 49.0002 | 2.15921 | ||||||||
\(516\) | −0.738844 | −0.0325258 | ||||||||
\(517\) | 15.9907 | 0.703270 | ||||||||
\(518\) | −9.55829 | −0.419967 | ||||||||
\(519\) | −3.65841 | −0.160586 | ||||||||
\(520\) | −9.97030 | −0.437227 | ||||||||
\(521\) | −6.54328 | −0.286666 | −0.143333 | − | 0.989675i | \(-0.545782\pi\) | ||||
−0.143333 | + | 0.989675i | \(0.545782\pi\) | |||||||
\(522\) | −12.4525 | −0.545032 | ||||||||
\(523\) | 0.573062 | 0.0250583 | 0.0125291 | − | 0.999922i | \(-0.496012\pi\) | ||||
0.0125291 | + | 0.999922i | \(0.496012\pi\) | |||||||
\(524\) | 1.00000 | 0.0436852 | ||||||||
\(525\) | 2.40635 | 0.105022 | ||||||||
\(526\) | −4.74709 | −0.206983 | ||||||||
\(527\) | 0.847195 | 0.0369044 | ||||||||
\(528\) | 0.331740 | 0.0144371 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −16.8676 | −0.732684 | ||||||||
\(531\) | 33.6101 | 1.45855 | ||||||||
\(532\) | −6.54454 | −0.283742 | ||||||||
\(533\) | −23.2608 | −1.00754 | ||||||||
\(534\) | −0.751179 | −0.0325067 | ||||||||
\(535\) | −27.6628 | −1.19597 | ||||||||
\(536\) | 8.82256 | 0.381077 | ||||||||
\(537\) | 2.01340 | 0.0868847 | ||||||||
\(538\) | −14.5561 | −0.627560 | ||||||||
\(539\) | 1.92398 | 0.0828717 | ||||||||
\(540\) | 3.34874 | 0.144107 | ||||||||
\(541\) | 19.7449 | 0.848898 | 0.424449 | − | 0.905452i | \(-0.360468\pi\) | ||||
0.424449 | + | 0.905452i | \(0.360468\pi\) | |||||||
\(542\) | −9.44993 | −0.405909 | ||||||||
\(543\) | −0.480069 | −0.0206017 | ||||||||
\(544\) | −5.26163 | −0.225590 | ||||||||
\(545\) | 38.2204 | 1.63718 | ||||||||
\(546\) | 1.63396 | 0.0699271 | ||||||||
\(547\) | 3.22818 | 0.138027 | 0.0690134 | − | 0.997616i | \(-0.478015\pi\) | ||||
0.0690134 | + | 0.997616i | \(0.478015\pi\) | |||||||
\(548\) | 6.34452 | 0.271025 | ||||||||
\(549\) | −12.1053 | −0.516642 | ||||||||
\(550\) | −8.68039 | −0.370133 | ||||||||
\(551\) | 9.68255 | 0.412490 | ||||||||
\(552\) | −0.180068 | −0.00766420 | ||||||||
\(553\) | 42.6645 | 1.81428 | ||||||||
\(554\) | 11.7380 | 0.498698 | ||||||||
\(555\) | −1.89112 | −0.0802736 | ||||||||
\(556\) | −0.627932 | −0.0266302 | ||||||||
\(557\) | 21.9754 | 0.931127 | 0.465563 | − | 0.885014i | \(-0.345852\pi\) | ||||
0.465563 | + | 0.885014i | \(0.345852\pi\) | |||||||
\(558\) | 0.477821 | 0.0202278 | ||||||||
\(559\) | 13.1274 | 0.555228 | ||||||||
\(560\) | −8.83879 | −0.373507 | ||||||||
\(561\) | 1.74549 | 0.0736948 | ||||||||
\(562\) | −5.06304 | −0.213572 | ||||||||
\(563\) | 36.7629 | 1.54937 | 0.774685 | − | 0.632347i | \(-0.217908\pi\) | ||||
0.774685 | + | 0.632347i | \(0.217908\pi\) | |||||||
\(564\) | 1.56294 | 0.0658116 | ||||||||
\(565\) | 47.5327 | 1.99972 | ||||||||
\(566\) | −3.36418 | −0.141407 | ||||||||
\(567\) | 24.7016 | 1.03737 | ||||||||
\(568\) | −3.83844 | −0.161057 | ||||||||
\(569\) | 23.2653 | 0.975332 | 0.487666 | − | 0.873030i | \(-0.337848\pi\) | ||||
0.487666 | + | 0.873030i | \(0.337848\pi\) | |||||||
\(570\) | −1.29485 | −0.0542351 | ||||||||
\(571\) | −24.4745 | −1.02423 | −0.512113 | − | 0.858918i | \(-0.671137\pi\) | ||||
−0.512113 | + | 0.858918i | \(0.671137\pi\) | |||||||
\(572\) | −5.89417 | −0.246448 | ||||||||
\(573\) | 0.323350 | 0.0135081 | ||||||||
\(574\) | −20.6210 | −0.860703 | ||||||||
\(575\) | 4.71170 | 0.196491 | ||||||||
\(576\) | −2.96758 | −0.123649 | ||||||||
\(577\) | −34.8341 | −1.45016 | −0.725082 | − | 0.688662i | \(-0.758198\pi\) | ||||
−0.725082 | + | 0.688662i | \(0.758198\pi\) | |||||||
\(578\) | −10.6847 | −0.444426 | ||||||||
\(579\) | −1.30065 | −0.0540530 | ||||||||
\(580\) | 13.0768 | 0.542986 | ||||||||
\(581\) | 41.5733 | 1.72475 | ||||||||
\(582\) | 0.0491518 | 0.00203741 | ||||||||
\(583\) | −9.97169 | −0.412985 | ||||||||
\(584\) | 3.38686 | 0.140149 | ||||||||
\(585\) | −29.5876 | −1.22330 | ||||||||
\(586\) | 24.6029 | 1.01634 | ||||||||
\(587\) | −40.8390 | −1.68561 | −0.842804 | − | 0.538221i | \(-0.819097\pi\) | ||||
−0.842804 | + | 0.538221i | \(0.819097\pi\) | |||||||
\(588\) | 0.188051 | 0.00775508 | ||||||||
\(589\) | −0.371533 | −0.0153088 | ||||||||
\(590\) | −35.2952 | −1.45308 | ||||||||
\(591\) | 2.75096 | 0.113159 | ||||||||
\(592\) | 3.37004 | 0.138508 | ||||||||
\(593\) | −13.2205 | −0.542901 | −0.271451 | − | 0.962452i | \(-0.587503\pi\) | ||||
−0.271451 | + | 0.962452i | \(0.587503\pi\) | |||||||
\(594\) | 1.97968 | 0.0812274 | ||||||||
\(595\) | −46.5064 | −1.90658 | ||||||||
\(596\) | −7.01246 | −0.287242 | ||||||||
\(597\) | −0.869045 | −0.0355676 | ||||||||
\(598\) | 3.19934 | 0.130831 | ||||||||
\(599\) | −2.11524 | −0.0864263 | −0.0432131 | − | 0.999066i | \(-0.513759\pi\) | ||||
−0.0432131 | + | 0.999066i | \(0.513759\pi\) | |||||||
\(600\) | −0.848425 | −0.0346368 | ||||||||
\(601\) | −20.1091 | −0.820269 | −0.410135 | − | 0.912025i | \(-0.634518\pi\) | ||||
−0.410135 | + | 0.912025i | \(0.634518\pi\) | |||||||
\(602\) | 11.6376 | 0.474311 | ||||||||
\(603\) | 26.1816 | 1.06620 | ||||||||
\(604\) | 10.1219 | 0.411854 | ||||||||
\(605\) | 23.7027 | 0.963653 | ||||||||
\(606\) | 0.310726 | 0.0126224 | ||||||||
\(607\) | −31.9652 | −1.29743 | −0.648715 | − | 0.761032i | \(-0.724693\pi\) | ||||
−0.648715 | + | 0.761032i | \(0.724693\pi\) | |||||||
\(608\) | 2.30746 | 0.0935799 | ||||||||
\(609\) | −2.14307 | −0.0868416 | ||||||||
\(610\) | 12.7122 | 0.514703 | ||||||||
\(611\) | −27.7694 | −1.12343 | ||||||||
\(612\) | −15.6143 | −0.631170 | ||||||||
\(613\) | 23.0258 | 0.930003 | 0.465001 | − | 0.885310i | \(-0.346054\pi\) | ||||
0.465001 | + | 0.885310i | \(0.346054\pi\) | |||||||
\(614\) | 22.2355 | 0.897353 | ||||||||
\(615\) | −4.07988 | −0.164517 | ||||||||
\(616\) | −5.22525 | −0.210531 | ||||||||
\(617\) | −23.0805 | −0.929185 | −0.464593 | − | 0.885524i | \(-0.653799\pi\) | ||||
−0.464593 | + | 0.885524i | \(0.653799\pi\) | |||||||
\(618\) | 2.83130 | 0.113892 | ||||||||
\(619\) | −48.1720 | −1.93619 | −0.968097 | − | 0.250575i | \(-0.919380\pi\) | ||||
−0.968097 | + | 0.250575i | \(0.919380\pi\) | |||||||
\(620\) | −0.501777 | −0.0201519 | ||||||||
\(621\) | −1.07457 | −0.0431210 | ||||||||
\(622\) | 21.8598 | 0.876499 | ||||||||
\(623\) | 11.8318 | 0.474033 | ||||||||
\(624\) | −0.576099 | −0.0230624 | ||||||||
\(625\) | −26.3584 | −1.05434 | ||||||||
\(626\) | −1.35107 | −0.0539996 | ||||||||
\(627\) | −0.765478 | −0.0305702 | ||||||||
\(628\) | −18.1972 | −0.726148 | ||||||||
\(629\) | 17.7319 | 0.707018 | ||||||||
\(630\) | −26.2298 | −1.04502 | ||||||||
\(631\) | 27.8966 | 1.11055 | 0.555273 | − | 0.831668i | \(-0.312614\pi\) | ||||
0.555273 | + | 0.831668i | \(0.312614\pi\) | |||||||
\(632\) | −15.0426 | −0.598361 | ||||||||
\(633\) | 2.72231 | 0.108202 | ||||||||
\(634\) | −13.8256 | −0.549086 | ||||||||
\(635\) | 11.5499 | 0.458342 | ||||||||
\(636\) | −0.974637 | −0.0386469 | ||||||||
\(637\) | −3.34118 | −0.132382 | ||||||||
\(638\) | 7.73067 | 0.306060 | ||||||||
\(639\) | −11.3909 | −0.450615 | ||||||||
\(640\) | 3.11636 | 0.123185 | ||||||||
\(641\) | 0.194820 | 0.00769494 | 0.00384747 | − | 0.999993i | \(-0.498775\pi\) | ||||
0.00384747 | + | 0.999993i | \(0.498775\pi\) | |||||||
\(642\) | −1.59840 | −0.0630838 | ||||||||
\(643\) | −13.8637 | −0.546732 | −0.273366 | − | 0.961910i | \(-0.588137\pi\) | ||||
−0.273366 | + | 0.961910i | \(0.588137\pi\) | |||||||
\(644\) | 2.83625 | 0.111764 | ||||||||
\(645\) | 2.30250 | 0.0906610 | ||||||||
\(646\) | 12.1410 | 0.477681 | ||||||||
\(647\) | 16.3051 | 0.641019 | 0.320510 | − | 0.947245i | \(-0.396146\pi\) | ||||
0.320510 | + | 0.947245i | \(0.396146\pi\) | |||||||
\(648\) | −8.70923 | −0.342131 | ||||||||
\(649\) | −20.8655 | −0.819044 | ||||||||
\(650\) | 15.0743 | 0.591264 | ||||||||
\(651\) | 0.0822327 | 0.00322295 | ||||||||
\(652\) | 1.13547 | 0.0444684 | ||||||||
\(653\) | −28.9898 | −1.13446 | −0.567229 | − | 0.823560i | \(-0.691985\pi\) | ||||
−0.567229 | + | 0.823560i | \(0.691985\pi\) | |||||||
\(654\) | 2.20843 | 0.0863566 | ||||||||
\(655\) | −3.11636 | −0.121766 | ||||||||
\(656\) | 7.27050 | 0.283865 | ||||||||
\(657\) | 10.0508 | 0.392118 | ||||||||
\(658\) | −24.6179 | −0.959705 | ||||||||
\(659\) | 11.8918 | 0.463239 | 0.231619 | − | 0.972806i | \(-0.425598\pi\) | ||||
0.231619 | + | 0.972806i | \(0.425598\pi\) | |||||||
\(660\) | −1.03382 | −0.0402415 | ||||||||
\(661\) | −16.8772 | −0.656448 | −0.328224 | − | 0.944600i | \(-0.606450\pi\) | ||||
−0.328224 | + | 0.944600i | \(0.606450\pi\) | |||||||
\(662\) | −0.802881 | −0.0312049 | ||||||||
\(663\) | −3.03122 | −0.117723 | ||||||||
\(664\) | −14.6578 | −0.568834 | ||||||||
\(665\) | 20.3952 | 0.790890 | ||||||||
\(666\) | 10.0009 | 0.387525 | ||||||||
\(667\) | −4.19619 | −0.162477 | ||||||||
\(668\) | 9.90036 | 0.383056 | ||||||||
\(669\) | 1.15428 | 0.0446269 | ||||||||
\(670\) | −27.4943 | −1.06220 | ||||||||
\(671\) | 7.51512 | 0.290118 | ||||||||
\(672\) | −0.510718 | −0.0197014 | ||||||||
\(673\) | 7.74456 | 0.298531 | 0.149266 | − | 0.988797i | \(-0.452309\pi\) | ||||
0.149266 | + | 0.988797i | \(0.452309\pi\) | |||||||
\(674\) | 20.0302 | 0.771535 | ||||||||
\(675\) | −5.06304 | −0.194877 | ||||||||
\(676\) | −2.76421 | −0.106316 | ||||||||
\(677\) | −7.87180 | −0.302538 | −0.151269 | − | 0.988493i | \(-0.548336\pi\) | ||||
−0.151269 | + | 0.988493i | \(0.548336\pi\) | |||||||
\(678\) | 2.74651 | 0.105479 | ||||||||
\(679\) | −0.774192 | −0.0297108 | ||||||||
\(680\) | 16.3971 | 0.628801 | ||||||||
\(681\) | −4.40535 | −0.168813 | ||||||||
\(682\) | −0.296637 | −0.0113588 | ||||||||
\(683\) | 47.6935 | 1.82494 | 0.912470 | − | 0.409144i | \(-0.134173\pi\) | ||||
0.912470 | + | 0.409144i | \(0.134173\pi\) | |||||||
\(684\) | 6.84756 | 0.261823 | ||||||||
\(685\) | −19.7718 | −0.755442 | ||||||||
\(686\) | 16.8918 | 0.644931 | ||||||||
\(687\) | −5.17736 | −0.197529 | ||||||||
\(688\) | −4.10314 | −0.156431 | ||||||||
\(689\) | 17.3168 | 0.659717 | ||||||||
\(690\) | 0.561156 | 0.0213629 | ||||||||
\(691\) | 14.8643 | 0.565463 | 0.282732 | − | 0.959199i | \(-0.408759\pi\) | ||||
0.282732 | + | 0.959199i | \(0.408759\pi\) | |||||||
\(692\) | −20.3169 | −0.772331 | ||||||||
\(693\) | −15.5063 | −0.589036 | ||||||||
\(694\) | −0.578901 | −0.0219748 | ||||||||
\(695\) | 1.95686 | 0.0742280 | ||||||||
\(696\) | 0.755599 | 0.0286409 | ||||||||
\(697\) | 38.2547 | 1.44900 | ||||||||
\(698\) | 25.7649 | 0.975215 | ||||||||
\(699\) | −2.87063 | −0.108577 | ||||||||
\(700\) | 13.3636 | 0.505095 | ||||||||
\(701\) | −13.4474 | −0.507900 | −0.253950 | − | 0.967217i | \(-0.581730\pi\) | ||||
−0.253950 | + | 0.967217i | \(0.581730\pi\) | |||||||
\(702\) | −3.43791 | −0.129756 | ||||||||
\(703\) | −7.77624 | −0.293287 | ||||||||
\(704\) | 1.84231 | 0.0694345 | ||||||||
\(705\) | −4.87068 | −0.183440 | ||||||||
\(706\) | 17.6860 | 0.665622 | ||||||||
\(707\) | −4.89426 | −0.184068 | ||||||||
\(708\) | −2.03941 | −0.0766456 | ||||||||
\(709\) | −36.2297 | −1.36063 | −0.680317 | − | 0.732918i | \(-0.738158\pi\) | ||||
−0.680317 | + | 0.732918i | \(0.738158\pi\) | |||||||
\(710\) | 11.9620 | 0.448924 | ||||||||
\(711\) | −44.6399 | −1.67413 | ||||||||
\(712\) | −4.17165 | −0.156339 | ||||||||
\(713\) | 0.161014 | 0.00603002 | ||||||||
\(714\) | −2.68721 | −0.100566 | ||||||||
\(715\) | 18.3683 | 0.686937 | ||||||||
\(716\) | 11.1814 | 0.417867 | ||||||||
\(717\) | −2.15702 | −0.0805553 | ||||||||
\(718\) | −11.8894 | −0.443708 | ||||||||
\(719\) | −26.6363 | −0.993367 | −0.496684 | − | 0.867932i | \(-0.665449\pi\) | ||||
−0.496684 | + | 0.867932i | \(0.665449\pi\) | |||||||
\(720\) | 9.24803 | 0.344654 | ||||||||
\(721\) | −44.5959 | −1.66084 | ||||||||
\(722\) | 13.6756 | 0.508954 | ||||||||
\(723\) | −1.34108 | −0.0498754 | ||||||||
\(724\) | −2.66605 | −0.0990828 | ||||||||
\(725\) | −19.7712 | −0.734283 | ||||||||
\(726\) | 1.36958 | 0.0508299 | ||||||||
\(727\) | 45.2769 | 1.67923 | 0.839614 | − | 0.543184i | \(-0.182781\pi\) | ||||
0.839614 | + | 0.543184i | \(0.182781\pi\) | |||||||
\(728\) | 9.07414 | 0.336310 | ||||||||
\(729\) | −25.2648 | −0.935734 | ||||||||
\(730\) | −10.5547 | −0.390646 | ||||||||
\(731\) | −21.5892 | −0.798506 | ||||||||
\(732\) | 0.734531 | 0.0271490 | ||||||||
\(733\) | −15.3558 | −0.567181 | −0.283591 | − | 0.958945i | \(-0.591526\pi\) | ||||
−0.283591 | + | 0.958945i | \(0.591526\pi\) | |||||||
\(734\) | −7.26661 | −0.268215 | ||||||||
\(735\) | −0.586034 | −0.0216162 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −16.2539 | −0.598719 | ||||||||
\(738\) | 21.5757 | 0.794214 | ||||||||
\(739\) | −21.0246 | −0.773403 | −0.386702 | − | 0.922205i | \(-0.626386\pi\) | ||||
−0.386702 | + | 0.922205i | \(0.626386\pi\) | |||||||
\(740\) | −10.5023 | −0.386071 | ||||||||
\(741\) | 1.32933 | 0.0488340 | ||||||||
\(742\) | 15.3515 | 0.563573 | ||||||||
\(743\) | 30.6421 | 1.12415 | 0.562076 | − | 0.827086i | \(-0.310003\pi\) | ||||
0.562076 | + | 0.827086i | \(0.310003\pi\) | |||||||
\(744\) | −0.0289934 | −0.00106295 | ||||||||
\(745\) | 21.8533 | 0.800645 | ||||||||
\(746\) | 13.5275 | 0.495278 | ||||||||
\(747\) | −43.4982 | −1.59152 | ||||||||
\(748\) | 9.69353 | 0.354431 | ||||||||
\(749\) | 25.1764 | 0.919926 | ||||||||
\(750\) | −0.161783 | −0.00590746 | ||||||||
\(751\) | 14.1536 | 0.516472 | 0.258236 | − | 0.966082i | \(-0.416859\pi\) | ||||
0.258236 | + | 0.966082i | \(0.416859\pi\) | |||||||
\(752\) | 8.67972 | 0.316517 | ||||||||
\(753\) | −1.55783 | −0.0567704 | ||||||||
\(754\) | −13.4250 | −0.488911 | ||||||||
\(755\) | −31.5435 | −1.14798 | ||||||||
\(756\) | −3.04775 | −0.110846 | ||||||||
\(757\) | 12.2832 | 0.446439 | 0.223220 | − | 0.974768i | \(-0.428343\pi\) | ||||
0.223220 | + | 0.974768i | \(0.428343\pi\) | |||||||
\(758\) | −12.8909 | −0.468219 | ||||||||
\(759\) | 0.331740 | 0.0120414 | ||||||||
\(760\) | −7.19088 | −0.260841 | ||||||||
\(761\) | −33.1950 | −1.20332 | −0.601659 | − | 0.798753i | \(-0.705493\pi\) | ||||
−0.601659 | + | 0.798753i | \(0.705493\pi\) | |||||||
\(762\) | 0.667368 | 0.0241762 | ||||||||
\(763\) | −34.7851 | −1.25931 | ||||||||
\(764\) | 1.79571 | 0.0649665 | ||||||||
\(765\) | 48.6597 | 1.75930 | ||||||||
\(766\) | 8.96319 | 0.323853 | ||||||||
\(767\) | 36.2350 | 1.30837 | ||||||||
\(768\) | 0.180068 | 0.00649764 | ||||||||
\(769\) | −5.22214 | −0.188315 | −0.0941577 | − | 0.995557i | \(-0.530016\pi\) | ||||
−0.0941577 | + | 0.995557i | \(0.530016\pi\) | |||||||
\(770\) | 16.2838 | 0.586826 | ||||||||
\(771\) | 0.563069 | 0.0202784 | ||||||||
\(772\) | −7.22308 | −0.259964 | ||||||||
\(773\) | −3.16545 | −0.113853 | −0.0569267 | − | 0.998378i | \(-0.518130\pi\) | ||||
−0.0569267 | + | 0.998378i | \(0.518130\pi\) | |||||||
\(774\) | −12.1764 | −0.437671 | ||||||||
\(775\) | 0.758649 | 0.0272515 | ||||||||
\(776\) | 0.272963 | 0.00979879 | ||||||||
\(777\) | 1.72114 | 0.0617456 | ||||||||
\(778\) | 28.0289 | 1.00488 | ||||||||
\(779\) | −16.7764 | −0.601076 | ||||||||
\(780\) | 1.79533 | 0.0642832 | ||||||||
\(781\) | 7.07158 | 0.253041 | ||||||||
\(782\) | −5.26163 | −0.188155 | ||||||||
\(783\) | 4.50909 | 0.161142 | ||||||||
\(784\) | 1.04433 | 0.0372976 | ||||||||
\(785\) | 56.7091 | 2.02403 | ||||||||
\(786\) | −0.180068 | −0.00642281 | ||||||||
\(787\) | 30.8609 | 1.10007 | 0.550036 | − | 0.835141i | \(-0.314614\pi\) | ||||
0.550036 | + | 0.835141i | \(0.314614\pi\) | |||||||
\(788\) | 15.2774 | 0.544233 | ||||||||
\(789\) | 0.854799 | 0.0304317 | ||||||||
\(790\) | 46.8780 | 1.66785 | ||||||||
\(791\) | −43.2604 | −1.53816 | ||||||||
\(792\) | 5.46718 | 0.194268 | ||||||||
\(793\) | −13.0507 | −0.463445 | ||||||||
\(794\) | −20.6532 | −0.732955 | ||||||||
\(795\) | 3.03732 | 0.107723 | ||||||||
\(796\) | −4.82621 | −0.171060 | ||||||||
\(797\) | −40.8799 | −1.44804 | −0.724020 | − | 0.689779i | \(-0.757708\pi\) | ||||
−0.724020 | + | 0.689779i | \(0.757708\pi\) | |||||||
\(798\) | 1.17846 | 0.0417171 | ||||||||
\(799\) | 45.6694 | 1.61567 | ||||||||
\(800\) | −4.71170 | −0.166584 | ||||||||
\(801\) | −12.3797 | −0.437414 | ||||||||
\(802\) | 21.1495 | 0.746814 | ||||||||
\(803\) | −6.23964 | −0.220192 | ||||||||
\(804\) | −1.58866 | −0.0560277 | ||||||||
\(805\) | −8.83879 | −0.311526 | ||||||||
\(806\) | 0.515139 | 0.0181450 | ||||||||
\(807\) | 2.62109 | 0.0922668 | ||||||||
\(808\) | 1.72561 | 0.0607066 | ||||||||
\(809\) | −40.7854 | −1.43394 | −0.716969 | − | 0.697106i | \(-0.754471\pi\) | ||||
−0.716969 | + | 0.697106i | \(0.754471\pi\) | |||||||
\(810\) | 27.1411 | 0.953641 | ||||||||
\(811\) | −29.2687 | −1.02776 | −0.513882 | − | 0.857861i | \(-0.671793\pi\) | ||||
−0.513882 | + | 0.857861i | \(0.671793\pi\) | |||||||
\(812\) | −11.9015 | −0.417659 | ||||||||
\(813\) | 1.70163 | 0.0596787 | ||||||||
\(814\) | −6.20865 | −0.217613 | ||||||||
\(815\) | −3.53853 | −0.123949 | ||||||||
\(816\) | 0.947450 | 0.0331674 | ||||||||
\(817\) | 9.46785 | 0.331238 | ||||||||
\(818\) | −7.40738 | −0.258993 | ||||||||
\(819\) | 26.9282 | 0.940948 | ||||||||
\(820\) | −22.6575 | −0.791234 | ||||||||
\(821\) | −22.0476 | −0.769468 | −0.384734 | − | 0.923028i | \(-0.625707\pi\) | ||||
−0.384734 | + | 0.923028i | \(0.625707\pi\) | |||||||
\(822\) | −1.14244 | −0.0398473 | ||||||||
\(823\) | 13.1850 | 0.459600 | 0.229800 | − | 0.973238i | \(-0.426193\pi\) | ||||
0.229800 | + | 0.973238i | \(0.426193\pi\) | |||||||
\(824\) | 15.7235 | 0.547755 | ||||||||
\(825\) | 1.56306 | 0.0544187 | ||||||||
\(826\) | 32.1228 | 1.11769 | ||||||||
\(827\) | 21.4821 | 0.747006 | 0.373503 | − | 0.927629i | \(-0.378156\pi\) | ||||
0.373503 | + | 0.927629i | \(0.378156\pi\) | |||||||
\(828\) | −2.96758 | −0.103130 | ||||||||
\(829\) | 34.7655 | 1.20746 | 0.603728 | − | 0.797190i | \(-0.293681\pi\) | ||||
0.603728 | + | 0.797190i | \(0.293681\pi\) | |||||||
\(830\) | 45.6791 | 1.58554 | ||||||||
\(831\) | −2.11363 | −0.0733210 | ||||||||
\(832\) | −3.19934 | −0.110917 | ||||||||
\(833\) | 5.49489 | 0.190387 | ||||||||
\(834\) | 0.113070 | 0.00391531 | ||||||||
\(835\) | −30.8531 | −1.06772 | ||||||||
\(836\) | −4.25105 | −0.147026 | ||||||||
\(837\) | −0.173020 | −0.00598046 | ||||||||
\(838\) | 31.3233 | 1.08205 | ||||||||
\(839\) | 32.3696 | 1.11752 | 0.558761 | − | 0.829329i | \(-0.311277\pi\) | ||||
0.558761 | + | 0.829329i | \(0.311277\pi\) | |||||||
\(840\) | 1.59158 | 0.0549148 | ||||||||
\(841\) | −11.3920 | −0.392827 | ||||||||
\(842\) | 25.1680 | 0.867345 | ||||||||
\(843\) | 0.911692 | 0.0314003 | ||||||||
\(844\) | 15.1183 | 0.520392 | ||||||||
\(845\) | 8.61428 | 0.296340 | ||||||||
\(846\) | 25.7577 | 0.885568 | ||||||||
\(847\) | −21.5723 | −0.741232 | ||||||||
\(848\) | −5.41261 | −0.185870 | ||||||||
\(849\) | 0.605780 | 0.0207903 | ||||||||
\(850\) | −24.7912 | −0.850331 | ||||||||
\(851\) | 3.37004 | 0.115524 | ||||||||
\(852\) | 0.691180 | 0.0236794 | ||||||||
\(853\) | 1.09492 | 0.0374893 | 0.0187447 | − | 0.999824i | \(-0.494033\pi\) | ||||
0.0187447 | + | 0.999824i | \(0.494033\pi\) | |||||||
\(854\) | −11.5696 | −0.395904 | ||||||||
\(855\) | −21.3395 | −0.729795 | ||||||||
\(856\) | −8.87665 | −0.303398 | ||||||||
\(857\) | −15.3754 | −0.525214 | −0.262607 | − | 0.964903i | \(-0.584582\pi\) | ||||
−0.262607 | + | 0.964903i | \(0.584582\pi\) | |||||||
\(858\) | 1.06135 | 0.0362339 | ||||||||
\(859\) | 39.1222 | 1.33483 | 0.667416 | − | 0.744685i | \(-0.267401\pi\) | ||||
0.667416 | + | 0.744685i | \(0.267401\pi\) | |||||||
\(860\) | 12.7869 | 0.436029 | ||||||||
\(861\) | 3.71317 | 0.126545 | ||||||||
\(862\) | −20.4496 | −0.696515 | ||||||||
\(863\) | −9.41233 | −0.320399 | −0.160200 | − | 0.987085i | \(-0.551214\pi\) | ||||
−0.160200 | + | 0.987085i | \(0.551214\pi\) | |||||||
\(864\) | 1.07457 | 0.0365576 | ||||||||
\(865\) | 63.3146 | 2.15276 | ||||||||
\(866\) | −13.6040 | −0.462281 | ||||||||
\(867\) | 1.92398 | 0.0653417 | ||||||||
\(868\) | 0.456676 | 0.0155006 | ||||||||
\(869\) | 27.7130 | 0.940099 | ||||||||
\(870\) | −2.35472 | −0.0798324 | ||||||||
\(871\) | 28.2264 | 0.956415 | ||||||||
\(872\) | 12.2645 | 0.415327 | ||||||||
\(873\) | 0.810038 | 0.0274156 | ||||||||
\(874\) | 2.30746 | 0.0780510 | ||||||||
\(875\) | 2.54824 | 0.0861463 | ||||||||
\(876\) | −0.609865 | −0.0206054 | ||||||||
\(877\) | 44.3929 | 1.49904 | 0.749520 | − | 0.661982i | \(-0.230284\pi\) | ||||
0.749520 | + | 0.661982i | \(0.230284\pi\) | |||||||
\(878\) | 9.19695 | 0.310382 | ||||||||
\(879\) | −4.43020 | −0.149427 | ||||||||
\(880\) | −5.74129 | −0.193539 | ||||||||
\(881\) | 39.9281 | 1.34521 | 0.672605 | − | 0.740001i | \(-0.265175\pi\) | ||||
0.672605 | + | 0.740001i | \(0.265175\pi\) | |||||||
\(882\) | 3.09914 | 0.104353 | ||||||||
\(883\) | −13.9955 | −0.470988 | −0.235494 | − | 0.971876i | \(-0.575671\pi\) | ||||
−0.235494 | + | 0.971876i | \(0.575671\pi\) | |||||||
\(884\) | −16.8337 | −0.566180 | ||||||||
\(885\) | 6.35553 | 0.213639 | ||||||||
\(886\) | 9.54765 | 0.320759 | ||||||||
\(887\) | −11.9828 | −0.402345 | −0.201172 | − | 0.979556i | \(-0.564475\pi\) | ||||
−0.201172 | + | 0.979556i | \(0.564475\pi\) | |||||||
\(888\) | −0.606836 | −0.0203641 | ||||||||
\(889\) | −10.5117 | −0.352552 | ||||||||
\(890\) | 13.0004 | 0.435773 | ||||||||
\(891\) | 16.0451 | 0.537530 | ||||||||
\(892\) | 6.41023 | 0.214631 | ||||||||
\(893\) | −20.0281 | −0.670215 | ||||||||
\(894\) | 1.26272 | 0.0422316 | ||||||||
\(895\) | −34.8451 | −1.16474 | ||||||||
\(896\) | −2.83625 | −0.0947526 | ||||||||
\(897\) | −0.576099 | −0.0192354 | ||||||||
\(898\) | −2.94871 | −0.0983999 | ||||||||
\(899\) | −0.675645 | −0.0225340 | ||||||||
\(900\) | −13.9823 | −0.466077 | ||||||||
\(901\) | −28.4791 | −0.948778 | ||||||||
\(902\) | −13.3945 | −0.445988 | ||||||||
\(903\) | −2.09555 | −0.0697355 | ||||||||
\(904\) | 15.2526 | 0.507295 | ||||||||
\(905\) | 8.30836 | 0.276179 | ||||||||
\(906\) | −1.82263 | −0.0605527 | ||||||||
\(907\) | −48.0125 | −1.59423 | −0.797114 | − | 0.603828i | \(-0.793641\pi\) | ||||
−0.797114 | + | 0.603828i | \(0.793641\pi\) | |||||||
\(908\) | −24.4650 | −0.811898 | ||||||||
\(909\) | 5.12087 | 0.169848 | ||||||||
\(910\) | −28.2783 | −0.937416 | ||||||||
\(911\) | 0.727120 | 0.0240906 | 0.0120453 | − | 0.999927i | \(-0.496166\pi\) | ||||
0.0120453 | + | 0.999927i | \(0.496166\pi\) | |||||||
\(912\) | −0.415500 | −0.0137586 | ||||||||
\(913\) | 27.0042 | 0.893710 | ||||||||
\(914\) | 27.5060 | 0.909817 | ||||||||
\(915\) | −2.28906 | −0.0756741 | ||||||||
\(916\) | −28.7523 | −0.950003 | ||||||||
\(917\) | 2.83625 | 0.0936613 | ||||||||
\(918\) | 5.65398 | 0.186609 | ||||||||
\(919\) | −32.2213 | −1.06288 | −0.531441 | − | 0.847095i | \(-0.678349\pi\) | ||||
−0.531441 | + | 0.847095i | \(0.678349\pi\) | |||||||
\(920\) | 3.11636 | 0.102743 | ||||||||
\(921\) | −4.00390 | −0.131933 | ||||||||
\(922\) | −37.7226 | −1.24233 | ||||||||
\(923\) | −12.2805 | −0.404217 | ||||||||
\(924\) | 0.940899 | 0.0309533 | ||||||||
\(925\) | 15.8786 | 0.522086 | ||||||||
\(926\) | 4.23431 | 0.139148 | ||||||||
\(927\) | 46.6608 | 1.53254 | ||||||||
\(928\) | 4.19619 | 0.137747 | ||||||||
\(929\) | −34.0838 | −1.11825 | −0.559126 | − | 0.829083i | \(-0.688863\pi\) | ||||
−0.559126 | + | 0.829083i | \(0.688863\pi\) | |||||||
\(930\) | 0.0903540 | 0.00296282 | ||||||||
\(931\) | −2.40976 | −0.0789766 | ||||||||
\(932\) | −15.9419 | −0.522195 | ||||||||
\(933\) | −3.93625 | −0.128867 | ||||||||
\(934\) | 18.2718 | 0.597872 | ||||||||
\(935\) | −30.2085 | −0.987925 | ||||||||
\(936\) | −9.49429 | −0.310331 | ||||||||
\(937\) | 8.24127 | 0.269231 | 0.134615 | − | 0.990898i | \(-0.457020\pi\) | ||||
0.134615 | + | 0.990898i | \(0.457020\pi\) | |||||||
\(938\) | 25.0230 | 0.817031 | ||||||||
\(939\) | 0.243284 | 0.00793928 | ||||||||
\(940\) | −27.0491 | −0.882245 | ||||||||
\(941\) | −2.75065 | −0.0896685 | −0.0448343 | − | 0.998994i | \(-0.514276\pi\) | ||||
−0.0448343 | + | 0.998994i | \(0.514276\pi\) | |||||||
\(942\) | 3.27674 | 0.106762 | ||||||||
\(943\) | 7.27050 | 0.236760 | ||||||||
\(944\) | −11.3258 | −0.368622 | ||||||||
\(945\) | 9.49788 | 0.308966 | ||||||||
\(946\) | 7.55925 | 0.245772 | ||||||||
\(947\) | −33.4469 | −1.08688 | −0.543439 | − | 0.839449i | \(-0.682878\pi\) | ||||
−0.543439 | + | 0.839449i | \(0.682878\pi\) | |||||||
\(948\) | 2.70868 | 0.0879739 | ||||||||
\(949\) | 10.8357 | 0.351743 | ||||||||
\(950\) | 10.8721 | 0.352736 | ||||||||
\(951\) | 2.48955 | 0.0807293 | ||||||||
\(952\) | −14.9233 | −0.483667 | ||||||||
\(953\) | 38.8227 | 1.25759 | 0.628795 | − | 0.777571i | \(-0.283549\pi\) | ||||
0.628795 | + | 0.777571i | \(0.283549\pi\) | |||||||
\(954\) | −16.0623 | −0.520037 | ||||||||
\(955\) | −5.59608 | −0.181085 | ||||||||
\(956\) | −11.9789 | −0.387426 | ||||||||
\(957\) | −1.39204 | −0.0449984 | ||||||||
\(958\) | 7.83957 | 0.253285 | ||||||||
\(959\) | 17.9947 | 0.581078 | ||||||||
\(960\) | −0.561156 | −0.0181112 | ||||||||
\(961\) | −30.9741 | −0.999164 | ||||||||
\(962\) | 10.7819 | 0.347623 | ||||||||
\(963\) | −26.3421 | −0.848863 | ||||||||
\(964\) | −7.44765 | −0.239873 | ||||||||
\(965\) | 22.5097 | 0.724614 | ||||||||
\(966\) | −0.510718 | −0.0164321 | ||||||||
\(967\) | 20.7530 | 0.667371 | 0.333686 | − | 0.942684i | \(-0.391708\pi\) | ||||
0.333686 | + | 0.942684i | \(0.391708\pi\) | |||||||
\(968\) | 7.60591 | 0.244463 | ||||||||
\(969\) | −2.18620 | −0.0702310 | ||||||||
\(970\) | −0.850650 | −0.0273127 | ||||||||
\(971\) | 47.8740 | 1.53635 | 0.768175 | − | 0.640240i | \(-0.221165\pi\) | ||||
0.768175 | + | 0.640240i | \(0.221165\pi\) | |||||||
\(972\) | 4.79196 | 0.153702 | ||||||||
\(973\) | −1.78097 | −0.0570954 | ||||||||
\(974\) | 2.46633 | 0.0790265 | ||||||||
\(975\) | −2.71440 | −0.0869305 | ||||||||
\(976\) | 4.07919 | 0.130572 | ||||||||
\(977\) | 1.85090 | 0.0592155 | 0.0296077 | − | 0.999562i | \(-0.490574\pi\) | ||||
0.0296077 | + | 0.999562i | \(0.490574\pi\) | |||||||
\(978\) | −0.204462 | −0.00653796 | ||||||||
\(979\) | 7.68545 | 0.245628 | ||||||||
\(980\) | −3.25452 | −0.103962 | ||||||||
\(981\) | 36.3957 | 1.16202 | ||||||||
\(982\) | −10.0832 | −0.321769 | ||||||||
\(983\) | −32.3375 | −1.03141 | −0.515703 | − | 0.856767i | \(-0.672469\pi\) | ||||
−0.515703 | + | 0.856767i | \(0.672469\pi\) | |||||||
\(984\) | −1.30918 | −0.0417352 | ||||||||
\(985\) | −47.6097 | −1.51697 | ||||||||
\(986\) | 22.0788 | 0.703132 | ||||||||
\(987\) | 4.43289 | 0.141100 | ||||||||
\(988\) | 7.38236 | 0.234864 | ||||||||
\(989\) | −4.10314 | −0.130472 | ||||||||
\(990\) | −17.0377 | −0.541494 | ||||||||
\(991\) | −35.5786 | −1.13019 | −0.565096 | − | 0.825025i | \(-0.691161\pi\) | ||||
−0.565096 | + | 0.825025i | \(0.691161\pi\) | |||||||
\(992\) | −0.161014 | −0.00511220 | ||||||||
\(993\) | 0.144573 | 0.00458789 | ||||||||
\(994\) | −10.8868 | −0.345308 | ||||||||
\(995\) | 15.0402 | 0.476806 | ||||||||
\(996\) | 2.63941 | 0.0836328 | ||||||||
\(997\) | 11.6446 | 0.368790 | 0.184395 | − | 0.982852i | \(-0.440968\pi\) | ||||
0.184395 | + | 0.982852i | \(0.440968\pi\) | |||||||
\(998\) | 26.8782 | 0.850814 | ||||||||
\(999\) | −3.62134 | −0.114574 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6026.2.a.i.1.14 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.i.1.14 | ✓ | 25 | 1.1 | even | 1 | trivial |